Calibration Method of Distance Between Optical Center of Camera and Rotation Axis in Rotating Vision Measurement System

Yanli Hou; Xianyu Su; Wenjing Chen

doi:10.3788/AOS202242.2112001

Acta Optica Sinica, Volume. 42, Issue 21, 2112001(2022)

Calibration Method of Distance Between Optical Center of Camera and Rotation Axis in Rotating Vision Measurement System

Yanli Hou, Xianyu Su, and Wenjing Chen^*

Department of Optic-Electronic, College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, Sichuan , China

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Figures & Tables(23)

Fig. 1. Schematic diagram of rotating vision measurement system

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Fig. 2. Imaging model. (a) Projection of coordinate system on XOZ plane; (b) projection of coordinate system on XOY plane

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Fig. 3. Position relationship between optical center of simulated camera and rotation center under different rotation angles. (a) 6°;(b) 12°; (c) 18°

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Fig. 4. Checkerboard images collected by simulated camera under different rotation angles

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Fig. 5. Checkerboards in field of view of simulated camera under different rotation angles. (a) 6°; (b) 12°; (c) 18°

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Fig. 6. Variation curve of distance between optical center of simulated camera and rotation center under linear model and distortion model

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Fig. 7. Distance variation curve

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Fig. 8. Experimental system

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Fig. 9. Collected target images

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Fig. 10. Positions of extracted feature points. (a) 0° initial position; (b) rotation angle of 12°

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Fig. 11. Curves of distance between optical center of camera and rotation center calculated by two methods

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Fig. 12. Coordinate values and 3D distribution map of optical center of camera. (a) Coordinate values of optical center of camera in three directions; (b) 3D distribution map of optical center of camera

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Table 1. Coordinates of optical center of simulated camera
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Table 1. Coordinates of optical center of simulated camera
Rotation angle /（°） Coordinates of optical center /mm
0 （-80， -50， 850）
6 （-80， -44.7736， 850.2739）
12 （-80， -39.6044， 851.0926）
18 （-80， -34.5492， 852.4472）

Table 2. Pixel coordinates of feature point pairs, corresponding spatial distance and distance between optical center of camera and rotation center under linear model

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Table 2. Pixel coordinates of feature point pairs, corresponding spatial distance and distance between optical center of camera and rotation center under linear model

Rotation angle /（°）	Coordinates of feature pairs before rotation /pixel	Coordinates of feature pairs after rotation /pixel	Spatial distance /mm	Distance l /mm
6	（1000， 810），（730， 810）	（805.79， 804.28），（541.27， 809.32）	135	50
6	（1030， 720），（790， 720）	（834.65， 715.55），（600.80， 718.71）	120	50
12	（1000， 810），（730， 810）	（616.59， 802.21），（351.12， 812.26）	135	50
12	（1030， 720），（790， 720）	（645.04， 713.71），（411.63， 719.98）	120	50
18	（1000， 810），（730， 810）	（427.79， 803.66），（154.86， 818.99）	135	50
18	（1030， 720），（790， 720）	（456.50， 714.35），（217.86， 723.87）	120	50

Table 3. Pixel coordinates of feature point pairs, corresponding spatial distance and distance between optical center of camera and rotation center under distortion model

View table

Table 3. Pixel coordinates of feature point pairs, corresponding spatial distance and distance between optical center of camera and rotation center under distortion model

Rotation angle /（°）	Coordinates of feature pairs before rotation /pixel	Coordinates of feature pairs after rotation /pixel	Spatial distance /mm	Distance l /mm
6	（999.62， 809.28），（729.91， 809.40）	（805.60， 803.68），（541.49， 808.65）	135	49.33
6	（1029.64， 719.50），（789.89， 719.70）	（834.50， 715.22），（600.86， 718.44）	120	49.02
12	（999.62， 809.28），（729.91， 809.40）	（616.66， 801.63），（351.99， 811.25）	135	48.94
12	（1029.64， 719.50），（789.89， 719.70）	（645.05， 713.47），（412.07， 719.49）	120	49.46
18	（999.62， 809.28），（729.91， 809.40）	（428.33， 802.84），（156.72， 817.65）	135	48.32
18	（1029.64， 719.50），（789.89， 719.70）	（456.80， 713.96），（219.27， 723.01）	120	49.12

Table 4. Average and standard deviation under different rotation angles
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Table 4. Average and standard deviation under different rotation angles
Index 6° 12° 18°
Average 49.84 50.09 50.12
Standard deviation 0.64 0.44 0.41

Table 5. Influence of simulated rotation angle error on calculation result of distance between optical center of camera and rotation center
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Table 5. Influence of simulated rotation angle error on calculation result of distance between optical center of camera and rotation center
Simulated rotation angle error /（°） 6° 12° 18°
0.005 49.19 49.60 49.74
-0.005 50.76 50.39 50.26

Table 6. Camera calibration results
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Table 6. Camera calibration results
Focal length /pixel Principal point /pixel Distortion coefficient Pixel error /pixel
f_x=1763.25， f_y=1764.13 u₀=629.74， v₀=489.04 k₁=-0.0476， k₂=0.2805， p₁=-0.0015， p₂=0.0016 0.0461， 0.0462

Table 7. Distance between optical center of camera and rotation center

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Table 7. Distance between optical center of camera and rotation center

Coordinates of feature point pairs before rotation /pixel	Coordinates of feature point pairs after rotation /pixel	Spatial distance /mm	Distance l /mm
（1157.1， 443.1），（903.4， 442.5）	（741.1， 443.4），（499.9， 441.4）	127.58	81.79
（1157.0， 471.4），（931.4， 527.4）	（741.0， 470.4），（527.3， 524.9）	116.89	81.72
（1157.4， 386.5），（931.6，442.5）	（741.2， 389.3），（527.4， 441.5）	116.89	81.81
（1129.4， 330.0），（988.4， 329.5）	（715.3， 334.5），（582.2， 331.6）	70.88	82.34
（1128.4， 584.2），（987.5， 584.0）	（714.6， 578.7），（581.6， 579.9）	70.88	81.99
（1072.6， 414.6），（959.9， 414.3）	（662.4， 415.4），（554.8， 414.1）	56.70	81.83
（1156.4， 668.9），（987.8， 499.2）	（740.5， 659.5），（581.7， 497.2）	120.28	82.53
（1156.5， 640.7），（987.8， 470.9）	（740.6， 632.4），（581.8， 469.6）	120.28	82.32
（1128.0， 697.1），（959.5， 527.4）	（714.5， 687.1），（554.5， 524.8）	120.28	81.77
（1156.3， 697.3），（903.2， 527.3）	（740.5， 686.5），（499.7， 524.9）	153.33	82.06

Table 8. Distance between optical center of camera and rotation center calculated by method in Ref. [20]
View table
Table 8. Distance between optical center of camera and rotation center calculated by method in Ref. [20]
Rotation angle /（°） 7.5 9.0 10.5 12.0 13.5 15.0 16.5 18.0 19.5 21.0
l_i/mm 82.14 82.01 81.79 81.98 82.39 82.27 82.02 82.09 82.45 82.42

Table 9. Calculated results of azimuth ω
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Table 9. Calculated results of azimuth ω
Rotation angle 7.5 9.0 10.5 12.0 13.5 15.0 16.5 18.0 19.5 21.0
ω 18.91 18.79 18.86 18.72 19.00 18.99 18.78 18.72 19.11 19.00

Table 10. Translation values ΔY_w and ΔZ_w in Y_w and Z_w directions
View table
Table 10. Translation values ΔY_w and ΔZ_w in Y_w and Z_w directions
Method ΔY_w ΔZ_w
Proposed method 26.56 77.60
Method based on coordinate transformation 26.60 77.73

Table 11. Standard deviation between optical center of camera and mass center
View table
Table 11. Standard deviation between optical center of camera and mass center
Direction X_w Y_w Z_w
Standard deviation /mm 0.15 0.09 0.16

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Yanli Hou, Xianyu Su, Wenjing Chen. Calibration Method of Distance Between Optical Center of Camera and Rotation Axis in Rotating Vision Measurement System[J]. Acta Optica Sinica, 2022, 42(21): 2112001

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Mar. 10, 2022

Accepted: May. 10, 2022

Published Online: Nov. 4, 2022

The Author Email: Chen Wenjing (chenwj0409@scu.edu.cn)

DOI:10.3788/AOS202242.2112001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Coordinates of optical center of simulated camera

Table 1. Coordinates of optical center of simulated camera

Table 2. Pixel coordinates of feature point pairs, corresponding spatial distance and distance between optical center of camera and rotation center under linear model

Table 2. Pixel coordinates of feature point pairs, corresponding spatial distance and distance between optical center of camera and rotation center under linear model

Table 3. Pixel coordinates of feature point pairs, corresponding spatial distance and distance between optical center of camera and rotation center under distortion model

Table 3. Pixel coordinates of feature point pairs, corresponding spatial distance and distance between optical center of camera and rotation center under distortion model

Table 4. Average and standard deviation under different rotation angles

Table 4. Average and standard deviation under different rotation angles

Table 5. Influence of simulated rotation angle error on calculation result of distance between optical center of camera and rotation center

Table 5. Influence of simulated rotation angle error on calculation result of distance between optical center of camera and rotation center

Table 6. Camera calibration results

Table 6. Camera calibration results

Table 7. Distance between optical center of camera and rotation center

Table 7. Distance between optical center of camera and rotation center

Table 8. Distance between optical center of camera and rotation center calculated by method in Ref. [20]

Table 8. Distance between optical center of camera and rotation center calculated by method in Ref. [20]

Table 9. Calculated results of azimuth ω

Table 9. Calculated results of azimuth ω

Table 10. Translation values ΔYw and ΔZw in Yw and Zw directions

Table 10. Translation values ΔYw and ΔZw in Yw and Zw directions

Table 11. Standard deviation between optical center of camera and mass center

Table 11. Standard deviation between optical center of camera and mass center

Table 10. Translation values ΔY_w and ΔZ_w in Y_w and Z_w directions

Table 10. Translation values ΔY_w and ΔZ_w in Y_w and Z_w directions